It would all depend on your focus and how well it would correlate with that of your advisor.
In general, standard textbooks would receive more citations than research papers. It would have a wider outreach (still dressing on the general case here). It would be pretty effective on the long run.
Coming back to your degree fulfilment, research papers would bring you closer to your immediate goal. This would quantify your achievements as a researcher and eventually qualify you for the degree.
Having stated above, the final decision is yours. If you are bent on finishing your degree quicker, resort to publishing research papers. If you wish for your career to develop in the future, then publishing a book would be a better option. This would accumulate your popularity while you work on your research papers afterwards. Also keep in mind the wavelength of your advisor.